CHARACTERIZATION OF COHESIVE BOND INTERFACES BETWEEN FRP AND UHPC UNDER MODE II LOADING USING FINITE ELEMENT METHODS

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1 Fourth Asia-Pacific Conference on FRP in Structures (APFIS 2013) December 2013, Melbourne, Australia 2013 International Institute for FRP in Construction CHARACTERIZATION OF COHESIVE BOND INTERFACES BETWEEN FRP AND UHPC UNDER MODE II LOADING USING FINITE ELEMENT METHODS D. Chen 1 and R. El-Hacha 1,2 1 Department of Civil Engineering, University of Calgary, Calgary, Alberta, Canada. 2 relhacha@ucalgary.ca ABSTRACT The behaviour of bond interfaces in composite structures is critical in the overall performance of the system. The ability to characterize and effectively approximate this behaviour without a considerable experimental sample size can be achieved through the use of finite element method software packages. This investigation will focus on the performance of double lap shear specimens, with Fibre Reinforced Polymer (FRP) plates bonded to Ultra-High Performance Concrete (UHPC) prism with an adhesively bonded aggregate interlock system. A finite element model will be developed to model the global behaviour of the specimens, which will then be validated using experimental test results. After model validation, the development of bond stresses leading up to damage initiation as well as during damage evolution will be evaluated and compared with the trends observed during experimental testing as well as those predicted using numerical methods. The influence on the overall structural behaviour due to areas that have reached maximum bond stress will be examined. The findings from this investigation will provide more clarity into the bond behaviour throughout the entire interface rather than at distinct and discontinuous locations, allowing for improved predictions for pre- and post-damage behaviour at material interfaces. KEYWORDS FRP, UHPC, bond, finite element, interfacial shear stress. INTRODUCTION Continued research into the development of optimized composite structural elements has led to many promising and feasible options that can perform as well as, if not better than, conventional construction materials, namely reinforced concrete and structural steel. The design of such composite structural element does involve an element of additional challenge, where a possible region of weakness can arise if the bond interface between adjacent materials has insufficient strength to ensure that the connected components perform as one entity. The body of research into the performance of cohesive bonds is diverse, ranging from the study of interlaminar interactions between neighbouring layers of Fibre Reinforced Polymer (FRP) sheets within a laminate sheet (Allix and Ladavèze, 1992; Hashemi et al., 1990), its potential as a connection method at attachment points between structural elements in modular construction (Nelson and Fam, 2013), and its application in hybrid structural elements composed of more than one material within its cross-section (Bakay et al., 2009). Note that the list above is by no means comprehensive and that numerous other branches exist in this field of research. Due to its importance, researchers have attempted to develop and characterize the behaviour of different types of bonding agents, through experimentation, modeling and numerical analysis (Keller and Gürtler, 2006; Sheppard et al., 1998; Reeder and Crews, 1990; Tvergaard and Hutchinson, 1996; Zuo, 1990; Cho et al., 2006; De Moura et al., 2008). Finite element modeling techniques have proven to be a useful tool in the design and analysis of structural elements that incorporate bond interfaces. Once validated with experimental results, the developed models can be applied towards the analysis of similar structural elements, without the need for additional experimentation. The goal of this paper is to determine the properties of the cohesive layer, a bonded silica sand layer, under pure Mode II loading. Due to the composite nature of the bond layer, experimental test results were compared with the finite element model analysis for validation of the results. Different approaches were used to evaluate the suitability of the model. Parameters that were investigated include: a) the usage of linear or quadratic elements, b) the accuracy of results obtained through a two-dimensional or three-dimensional model and c) the idealization

2 of the bond layer using cohesive elements compared with using an interaction with cohesive properties. In addition, a closer inspection of the results obtained from the finite element analysis was taken to observe the progression of crack propagation and the distribution of stresses along the bond interface. At the end of the study, a recommended set of parameters are offered that will provide the optimum combination of accuracy and required computational energy and time. BACKGROUND INFORMATION The experimental program was conducted on double shear bond specimens. A thin layer of silica sand was bonded to the coarsened surface of a pultruded Glass FRP (GFRP) plate. The epoxy adhesive used for bonding of the silica sand was a moisture insensitive epoxy adhesive originally intended for bonding between hardened concrete and steel. After allowing for a seven day curing time, two of the prepared GFRP plates were bonded directly to a cast-in-place Ultra-High Performance Concrete (UHPC) prism, to two of its opposing sides. The configuration of the test specimen is shown in Figure 1. Figure 1. Configuration and dimensions of the double shear bond specimens (Chen and El-Hacha, 2012) The specifics details relating to the experimental program and its results were described in detail in a separate publication and will not be repeated here in this paper (Chen and El-Hacha, 2012; Chen and El-Hacha, 2011). Only key results required in order to construct the finite element (FE) model will be presented. FINITE ELEMENT ANALYSIS Model development The FE model was developed using ABAQUS 6.9. The material properties for the pultruded GFRP plate are provided in Table 1. The associated parameters for cohesive elements obtained from a related preliminary study regarding the behaviour of full length hybrid FRP-UHPC beams (Chen and El-Hacha, 2011), based on the method introduced by Diehl (2008), are provided in Table 2, along with the material properties for the UHPC. The test matrix showing the different developed models and their designation IDs is shown in Table 3. Table 1. GFRP material properties. (Chen and El-Hacha, 2011) Parameters Value Longitudinal modulus MPa Transverse modulus 6890 MPa Longitudinal tensile strength 207 MPa Longitudinal compressive strength 207 MPa Transverse tensile strength 48.3 MPa Transverse compressive strength 103 MPa Longitudinal shear strength 31 MPa Transverse shear strength 31 MPa Poisson s ratio 0.33

3 Table 2. Cohesive parameters and UHPC material properties. (Chen and El-Hacha, 2011) Parameters Value UHPC Young s modulus MPa UHPC Poisson s ratio 0.2 Cohesive shear stress 6 MPa Cohesive shear fracture energy 1.2 J/m 2 Cohesive penalty normal stiffness MPa Cohesive shear stiffness 300 MPa Table 3. Model designation IDs. Model description 2D model with linear elements (cohesive elements) 2D model with quadratic elements (cohesive elements) 3D model with linear elements (cohesive elements) 3D model with quadratic elements (cohesive elements) 2D model with linear elements (cohesive interaction) 2D model with quadratic elements (cohesive interaction) Designation ID 2D-L-CE 2D-Q-CE 3D-L-CE 3D-Q-CE 2D-L-CI 2D-Q-CI In the developed models, either plane stress bilinear or bi-quadratic elements were used to represent the GFRP and UHPC materials, along with four-noded cohesive elements or a cohesive interaction used to idealize the bond layer. The GFRP plate was modeled using 3 layers of elements, the UHPC prism modeled with 19 element layers and the cohesive layer modeled as a single layer of cohesive elements. The approximate size of the mesh along the length of the specimen is 4 mm. Due to symmetry of the specimen dimensions as well as the applied load, only one-half of the specimen was modeled, with the appropriate boundary conditions used at the lines of symmetry to restrict the degrees of freedom. A diagram of the FE model is provided in Figure 2. Comparison of model accuracies Figure 2. Diagram of the developed finite element model As a general validation method, the results obtained from the four FE models performed using the cohesive elements were first compared with the experimental load-deflection curves of the three bond specimens tested. The graphical comparison is shown in Figure Applied Shear Load (kn) Specimen 1 Specimen 2 Specimen 3 2D-L-CE 2D-Q-CE 3D-L-CE 3D-Q-CE Slippage (mm) Figure 3. Comparison of FE models with cohesive elements with experimental data.

4 From the results, it is evident that the use of more complex and computationally intensive models do not provide any additional increase in the accuracy, in terms of the analysis results for global response. All of the loaddeflection curves derived from the FE analysis essentially overlap one another and as a group, shows a lower stiffness and maximum load reached than the tested specimens. The accuracy of the FE analysis in relation to the actual experimental results is quite acceptable, with a percent error for the maximum load of approximately 15%. Judging from the similarity of the FE analysis regardless of the dimension and element type used, for further analysis, the simpler two-dimensional FE model using linear elements will be used. Comparison between cohesive elements and cohesive interactions Using the penalty-based cohesive zone finite element approach proposed by Diehl (2008), it imposes a large number of simplifying assumptions and limitations on the parameters used in order to model the cohesive behaviour solely based on the fracture energy. By modeling the interface as a layer of cohesive elements with a quantifiable thickness, one of the required parameters is the specification of the cohesive layer stiffness. This parameter is not explicitly necessary when the cohesive layer is defined as a cohesive interaction, which idealizes the bond layer as a zero-thickness area, and allows for the substitution of element stiffness values with a contact enforcement criteria. The last pairs of FE models conducted were performed by replacing the layer of cohesive elements with an equivalent cohesive interaction between the upper FRP plate and the lower UHPC prism. The global loaddeflection curves of models 2D-L-CE, 2D-L-CI, and 2D-Q-CI are compared in Figure Applied Shear Load (kn) D-L-CE 2D-L-CI 2D-Q-CI Slippage (mm) Figure 4. Comparison of behaviour using cohesive elements and cohesive interaction. From the comparison shown in Figure 4, it is evident that the substitution of cohesive elements with a cohesive interaction results in noticeably different behaviour in the load-deflection of the double shear specimens prior to the initiation of crack growth, where the stiffness of the specimen appears to be nearly infinite prior to crack initiation. This is to be expected since the contact enforcement criteria would assume complete contact and zero relative movement above and below the interface prior to reaching the limiting shear stress. It appears that the use of contact interactions should not be applied when linear elements are used for modeling the material adjacent to the interface, as it leads to irregular digressions in the load-deflection behaviour. Nevertheless, it is worth noting that as the load approaches the critical failure load, both methods converge to the same point. Thus, if the aim of the model is to determine the ultimate behaviour of the system, without granting heavy importance on the behaviour of the system during the initial loading prior to cracking, then a model using a cohesive interaction rather than a layer of cohesive elements would provide similar, if not identical, solutions. INVESTIGATION OF CRACK GROWTH AND INTERFACE SHEAR STRESS To track the progress of crack growth along the interface, snapshots of the shear stress within the area of interest at regular load intervals are provided for model 2D-L-CE and model 2D-Q-CI in Figures 5 a) and b), respectively. The color scaling provided in both figures are consistent, where the blue regions indicate the highest stress concentration, which is approximately equal to 6 MPa, the ultimate shear stress of the interface. For reference to approximate dimensions, a scale is provided at the bottom of both figures.

5 Comparisons between the crack progression shown in Figures 4 indicate that, in general, the location of the peak stress, and thus the location of the crack locus, is consistent between the two models. It can be noted that, in the case of model 2D-Q-CI where the cohesive interaction was used to model the interface, uneven stress fields are evident in the surrounding materials, particularly where high stress gradients are present. For model 2D-L-CE, the cohesive element layer provides consistent cohesive layer nodes locations that line up with the nodes of the adjoining materials, leading to the smooth stress fields seen in Figure 5a. (a) (b) Figure 5. Shear stress concentration plot of model (a) 2D-L-CE and (b) 2D-Q-CI at loads (from top to bottom) of 80 kn, 120 kn, 140 kn and 160 kn. The detailed investigation into the stress and crack growth during loading shows that crack initiation would commence at a load level of 80 kn, reaching an ultimate load of approximately 160 kn. At the ultimate condition immediately prior to failure, the crack would extend to a length of around 180 mm along the interface. It should be noted that, since the two-dimensional models used for this part of the investigation was performed using plane stress elements, the location of the crack front obtained would be correlated to the crack location at the outer edges of the cohesive layer in the equivalent three-dimensional model. This is due to the fact that, in three-dimensional space, the crack front along the entire width of the specimen would be parabolic in shape, where the crack location in the interior of the interface would lag behind the crack location at the edges. This behaviour is shown in Figure 6. CONCLUSIONS. Figure 6. Shape of crack front in a three-dimensional model. This investigation into the FE modeling of a double shear bond specimen loaded under pure Mode II conditions can provide the following conclusions: There is no discernible advantage in the use of higher order elements in the FE analysis when cohesive elements are used; Simplification of the analysis into a two-dimensional model will provide near similar results to those obtained from a three-dimensional model;

6 The penalty-based cohesive zone finite element approach proposed by Diehl [18] performs well and provides accurate results when compared with experimental data; The use of a cohesive interaction to model the interface layer requires higher order elements to be used in the surrounding material in order to prevent irregularities in the obtained behaviour; Modeling with cohesive elements rather than a cohesive interaction will allow for smooth stress fields in the adjacent bonded materials; and, The locus of the crack front determined from models using both cohesive elements and cohesive interaction are equivalent. From the summarized results, it is recommended for future FE model developments of this kind to use a layer of linear cohesive elements to represent the bond interface, since it provides superior and consistent results on both the local and global scales. The use of the cohesive interaction method, which assumes an initial contact enforcement criteria, would only be recommended for use in preliminary studies or in the case where the global behaviour at the ultimate load condition is desired. ACKNOWLEDGEMENTS The authors would like to thank Lafarge Canada and Sika Canada Inc. for their generous donations of materials used. We would also like to acknowledge the University of Calgary and the Natural Sciences and Engineering Research Council of Canada (NSERC) for their financial support towards this research project. REFERENCES Allix, O. and Ladavèze, P. (1992). Interlaminar interface modeling for the prediction of delamination, Composite Structures, 22, Bakay, R., Sayed-Ahmed, E.Y. and Shrive, N.G. (2009). Interfacial debonding failure for reinforced concrete beams strengthened with carbon-fibre-reinforced polymer strips, Canadian J. of Civil Eng., 36(1), Chen, D. and El-Hacha, R. (2012). Bond strength between cast-in-place ultra-high-performance-concrete and glass fibre reinforced polymer plate using epoxy bonded coarse silica sand, Journal of ASTM International, 9(3), 17p. Chen, D. and El-Hacha, R. (2011) Investigation of contact behaviour in hybrid FRP-UHPC beams using finite element methods, Proceedings of the ACI Fall 2012 Convention. Cho, K., Cho, J-R., Chin, W-J. and Kim, B-S. Bond-slip model for coarse sand coated interface between FRP and concrete from optimization technique, Computers & Structures, 84(7), Correia, J.R., Branco, F.A. and Ferreira, J.G. (2007). Flexural behaviour of GFRP-concrete hybrid beams with interconnection slip, Composite Structures, 77(1), De Moura, M.F.S.F., Gonçalves, J.P.M., Chousal, J.A.G. and Campilho, R.D.S.G. (2008). Cohesive and continuum mixed-mode damage models applied to the simulation of the mechanical behaviour of bonded joints, International Journal of Adhesion and Adhesives, 28(8), Diehl, T. (2008). On using a penalty-based cohesive-zone finite element approach, Part I: Elastic solution benchmarks, International Journal of Adhesion and Adhesives, 28(4-5), Hashemi, S., Kinloch, A.J. and Williams, J.G. (1992). The analysis of interlaminar fracture in uniaxial fibrepolymer composites, Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences, 427(1872), Hassan, T. and Rizkalla, S. (2007). Investigation of bond in concrete structures strengthened with near surface mounted carbon fiber reinforced polymer strips, Journal of Composites for Construction, 7(3), Keller, T. and Gürtler, H. (2006). Design of hybrid bridge girders with adhesively bonded and compositely acting FRP deck, Composite Structures, 74(2), Lu, X.Z., Teng, J.G., Ye, L.P. and Jiang, J.J. (2005). Bond-slip model for FRP sheets/plates bonded to concrete, Engineering Structures, 26(6), Nelson, M. and Fam, A. (2013). Structural GFRP permanent forms with T-shape ribs for bridge decks supported by precast concrete girders, Journal of Bridge Engineering, Vol. 18, Issue 9, Sept Mi, Y., Crisfield, M.A., Davies, G.A.O and Hellweg, H.B. (1998). Progressive delamination using interface elements, Journal of Composite Materials, 32(14), Reeder, J.R. and Crews, J.R. Jr. (1990). Mixed-mode bending method for delamination testing, American Institute of Aeronautics and Astronautics Journal, 28(7), Sheppard, A., Kelly, D. and Tong, L. (1998). A damage zone model for the failure analysis of adhesively bonded joints, International Journal of Adhesion and Adhesives, 18(6), Suo, Z. (1990). Failure of brittle adhesive joints, Applied Mechanics Reviews, 43(5), S276. Tvergaard, V. and Hutchinson, J.W. (1996). On the toughness of ductile adhesive joints, Journal of the Mechanics and Physics of Solids, 44(5),